The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $$6.00$, and bags of cookies cost $$4.50$, and sales equaled $$30.00$ in total. There were $2$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the drama club.
Explanation: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${6x+4.5y = 30}$ ${y = x+2}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+2}$ for $y$ in the first equation. ${6x + 4.5}{(x+2)}{= 30}$ Simplify and solve for $x$ $ 6x+4.5x + 9 = 30 $ $ 10.5x+9 = 30 $ $ 10.5x = 21 $ $ x = \dfrac{21}{10.5} $ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $ {y = x+2}$ to find $y$ ${y = }{(2)}{ + 2}$ ${y = 4}$ You can also plug ${x = 2}$ into $ {6x+4.5y = 30}$ and get the same answer for $y$ ${6}{(2)}{ + 4.5y = 30}$ ${y = 4}$ $2$ bags of candy and $4$ bags of cookies were sold.